500 is decreased by 40%. The result is then decreased by 40%, and so on. In total, the decrease is applied 10 times. Write an expression to represent the final result of this process.
Answers
The final result of this process is roughly 3.0233.
To represent the final result of the described process, we can use the conception of emulsion chance drop.
Each time a drop of 40 is applied, the remaining value is equal to
60( 100- 40) of the former value.
Since the drop is applied 10 times, we can express the final result as follows
Final Result = 500 *(0.6) 10
Then, 500 represents the original value, and(0.6) 10 represents the emulsion drop applied 10 times.
The value0.6 represents 60 as a numeric.
To calculate the final result, simply estimate the expression using a calculator or by performing the exponentiation
Final Result ≈ 500 *0.0060466 ≈3.0233
Thus, after the drop is applied 10 times, the final result of this process is roughly 3.0233.
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Related Questions
Express the ratio below in its simplest form
12:6
Answers
Answer:
12/6 simplified to lowest terms is 2/1.
Step-by-step explanation:
Divide both the numerator and denominator by the HCF
12 ÷ 6
6 ÷ 6
Reduced fraction:
12/6 simplified to lowest terms is 2/1.
Answer: 2:1
Step-by-step explanation:
12:6
Both left and right can be divided by 6, like a fraction, reduce.
= 2:1
A 55.9-kg hiker ascends a 46.6-meter high hill at a constant speed of 1.0 m/s. If it takes 373 s to climb the hill, then determine the power delivered by the hiker.
Answers
Step 1
State formula for Power
\(\begin{gathered} \text{Power =}\frac{work}{\Delta time} \\ \text{But work = Force(F)}\times Dis\tan ce(S)\text{ for rectilinear motion} \\ \end{gathered}\)Hence,
\(\begin{gathered} \text{Power}=\frac{F\times S}{\Delta Time(t)} \\ \text{Also Force(F) for rectilinear motion}=\text{Mass(M)}\times acceleration(a) \\ \text{Hence,} \\ \text{Power}=\text{ }\frac{M\times a\times S}{\Delta t} \end{gathered}\)Step 2
Determine the power delivered by the hiker.
\(\begin{gathered} \text{Power}=\frac{M\times a\times S}{\Delta t} \\ M=\text{mass = 55.9kg} \\ a=\text{ rectilinear acc}eleration\text{ = 1.0m/s} \\ S=\text{distance}=46.6m \\ \Delta t=373s \end{gathered}\)\(\begin{gathered} \text{Power}=\frac{55.9\times1.0\times46.6}{373} \\ \end{gathered}\)\(\begin{gathered} \text{Power}=6.983753351 \\ \text{Power }\approx\text{ 6.984 Joules(J)/Seconds(s) or Watts(w) to 3 decimal places} \\ \end{gathered}\)Hence the power delivered by the hiker to 3 decimal places is approximately 6.984 J/s or watts
what is 80 cents + 45 cents
Answers
Answer: 1.25
Step-by-step explanation:
$0.80
$0.45 (when adding 8+4 you carry the 1 from 12 to the 0s
-------------
1 . 2 5
Question 3 math help please show work
Answers
Answer:
\(17.3\:\mathrm{m}\)
Step-by-step explanation:
The circumference of a circle is given by \(C=2r\pi\), where \(r\) is the radius of the circle.
By definition, the radius is equal to half the diameter. Therefore, a circle with a diameter of 5.5 meters has a radius of \(5.5\cdot \frac{1}{2}=2.75\) meters.
Thus, the circumference of the silo must be:
\(C=2\cdot 2.75\cdot \pi=17.2787595947\approx \boxed{17.3\:\mathrm{m}}\)(rounded to one decimal place as requested by question).
*Units for circumference should be in the same units as the radius/diameter is given in, since the circumference just refers to the perimeter of a circle.
**Your work for question 2 should include an equals sign, not an addition sign, between the part where you're adding the sevens and multiplying them: \(\implies 7+7+7+7+7+7\boxed{=}7\cdot 6\)
What is the value today of a money machine that will pay\$1000 per year for 6 years? Assume the first payment is made two year from today and interest rate is 4%
4712.25
4885.32
4990.25
5040.52
Question 10 (1 point) You have invested your money into a project that will pay you $500 at monthly frequency starting 4 years from today and will continue to pay out forever. If the interest rate is 12% p.a., then the value of your investment today (t=0) is $
20212.04
31323.15
42434.26
53545.37
Answers
The value today of a money machine is $4,712.25. The value of the investment is $31,323.15.
Question 9:
To calculate the present value of the money machine, we can use the formula for the present value of an ordinary annuity:
PV = P * [(1 - (1 + r)^(-n)) / r],
where PV is the present value, P is the annual payment, r is the interest rate per period, and n is the number of periods.
Given:
Annual payment (P) = $1000,
Interest rate per period (r) = 4% = 0.04,
Number of periods (n) = 6 - 2 = 4.
Plugging in the values, we get:
PV = $1000 * [(1 - (1 + 0.04)^(-4)) / 0.04] = $4712.25.
Therefore, the value today of the money machine is $4712.25.
Question 10:
To calculate the present value of the investment, we can use the formula for the present value of a perpetuity:
PV = P / r,
where PV is the present value, P is the periodic payment, and r is the interest rate per period.
Given:
Periodic payment (P) = $500,
Interest rate per period (r) = 12% / 12 = 0.12 / 12 = 0.01.
Plugging in the values, we get:
PV = $500 / 0.01 = $31,500.
Therefore, the value of the investment today is $31,323.15.
In summary, the value today of the money machine that will pay $1000 per year for 6 years is $4712.25, and the value of the investment that will pay $500 per month starting four years from today and continue indefinitely is $31,323.15.
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A pond contains 20 tadpoles, of which f are frog tadpoles and the others are toad tadpoles. If 10 more frog tadpoles are added to the pond, the probability of catching a frog tadpole is doubled. Find f
Answers
Answer:
The value of f is 5
Step-by-step explanation:
Initially, the number of frog tadpoles = f
The initial probability of catching a frog tadpole = f/20
Adding 10 more frog tadpoles,
Number of frog Tadpoles = f +10
Total number of tadpoles in the pond = 20+10 = 30
new probability of catching a frog tadpole = (f+10)/30
New probability of catching a frog tadpole = 2 x Initial probability of catching a frog tadpole
(f+10)/30 = 2 x (f/20)
(f+10)/30 = f/10
f+10 = f x 30/10
f+10 = 3f
2f = 10
f = 5
What is the equity multiplier?
Answers
on solving the provided question we can say that A larder equity multiplier indicates a greater reliance on debt financing.
what is multiply?Along with addition, subtraction, and division, multiplication is one of the four arithmetic operations. Multiplication in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals product. Specifically, multiplicand: First number (factor). divider:
A financial ratio called the equity multiplier gauges how much debt is being used to fund a company's assets in comparison to its owners' equity. It is determined by dividing the total assets by the entire equity of the organization.
Total Assets / Total Equity is the equity multiplier.
A larder equity multiplier indicates a greater reliance on debt financing. The equity multiplier measures the proportion of a company's assets that are funded by debt. Analysts and investors frequently use it to assess a company's financial leverage and risk profile since businesses with higher debt levels may be more susceptible to changes in interest rates, the state of the economy, or other external variables.
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we call a number a mountain number if its middle digit is larger than any other digit. for example, 284 is a mountain number. how many 3-digit mountain numbers are there?
Answers
If we consider a mountain number with its middle digit is larger than any other digit, then there are possible three-digit mountain numbers are equals the 240.
A number is called a 'mountain' if its decimal digits insitiate with 1, i.e. 'base camp', increase continuously to one largest digit, then decrease continuously back to one i.e. back to base camp. We have a number is called a mountain number. Now, there are 100 to 999 total 3-digit numbers. Now, with 2 in the middle, we have = 2 numbers[1 x 2] - 120 = 121
With 3 in the we have = 6 numbers[2 x 3] - 130, 131, 132, 230, 231, 232.......and so on.With 4 in the middle,we have = 12 numbers[3 x4]With 5 in the middle, we have = 20 numbers[4 x 5]With 6 in the middle, we have = 30 numbers[5 x 6]With 7 in the middle, we have = 42 numbers[6 x 7]With 8 in the middle, we have = 56 numbers[7 x 8]With 9 in the middle, we have = 72 numbers[8 x 9]So, we have a total of Total Number = 2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 = 240 "mountain numbers". Hence, the required number , value is 240.
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Carmen can type 18 words in 27 seconds. How many words can she type in 60 seconds?
Answers
Answer:
40words
Step-by-step explanation:
Answer: 40
Step-by-step explanation: I Took The Test
A philanthropic organization sent free mailing labels and greeting cards to a random sample of 100,000 potential donors on their mailing list and received 5069 donations. They have had a contribution rate of 5% in past campaigns, but a staff member hopes that the rate will be higher if they run this campaign as currently designed. Complete parts a through c below. Assume the independence assumption is met. a) What are the hypotheses?
Answers
The hypotheses for this scenario are as follows: Null Hypothesis (H₀): The contribution rate for the current campaign is 5%. Alternative Hypothesis (H₁): The contribution rate for the current campaign is higher than 5%. These hypotheses represent the comparison between the expected contribution rate based on past campaigns and the potential higher contribution rate for the current campaign.
The hypotheses for this scenario can be stated as follows:
Null Hypothesis (H₀): The contribution rate for the current campaign is the same as the previous campaigns, i.e., 5%.
Alternative Hypothesis (H₁): The contribution rate for the current campaign is higher than 5%.
These hypotheses reflect the staff member's hope that the current campaign will yield a higher contribution rate compared to the past campaigns.
The null hypothesis assumes no difference in the contribution rate, while the alternative hypothesis suggests an increase in the contribution rate.
The objective is to test whether there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis and conclude that the current campaign has a higher contribution rate.
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You deposit $2,000 in a savings account that earns 5% simple interest yearly. How many years will it take to triplicate your money? (Where applicable use the rule of 72 ). Usted deposita $2,000 en una cuenta de ahorros que paga 5% de interés simple anual. ¿Cuántos años le tomará triplicar su dinero? (Si aplica utilice la regla del 72). 12.05 años| 11.34 años 40 años 25 años
Answers
Answer:
Scroll Down Below...
Step-by-step explanation:
To decide by virtue of what many age it will love trio person engaged in private ownership of business, we can use the rule of 72 for plain interest. The rule of 72 states that you can approximate the number of age it takes for an expenditure to double by separating 72 apiece annual interest. In this case, we ask about by virtue of what long it takes to trio person engaged in private ownership of business, so we'll separate 72 for one interest (5%).72 / 5 = 14.4According to the rule of 72, it would take nearly 14.4 age to double person engaged in private ownership of business at a 5% annual interest. Since we be going to trio person engaged in private ownership of business, we need to double it two times.14.4 age x 2 = 28.8 ageTherefore, it would take nearly 28.8 age to trio person engaged in private ownership of business at a 5% natural interest.In Spanish:Para determinar cuántos años tomará triplicar el money, podemos utilizar la regla del 72 para el interés plain. La regla del 72 establece que puedes aproximar el número de años que se tarda en duplicar una inversión dividiendo 72 entre la tasa de interés anual. En este caso, queremos weapon cuánto tiempo tomará triplicar el money, así que dividiremos 72 entre la tasa de interés (5%).72 / 5 = 14.4Según la regla del 72, tomaría aproximadamente 14.4 años duplicar el money a una tasa de interés anual del 5%. Como queremos triplicar el money, necesitamos duplicarlo do veces.14.4 años x 2 = 28.8 añosPor lo tanto, tomaría aproximadamente 28.8 años triplicar el money a una tasa de interés natural del 5%. La respuesta correcta es 28.8 años.
3 Jason's high school played fifteen hockey games this year and three were at night. The team won most of theirgames. They were defeated during four games. How many games did they win ?
Answers
they played 15 games
they were defeated during four games
\(x=15-4\)\(x=11\)they won 11 games
15-4=11
A random variable is normally distributed with a mean of ? = 50 and a standard deviation of ? = 5.
a. What is the probability the random variable will assume a value between 45 and 55 (to 4 decimals)?
b. What is the probability the random variable will assume a value between 40 and 60 (to 4 decimals)?
Answers
a. There is a 0.6827 percent chance that the random variable will take on a value between 45 and 55. b. There is a 0.9545 percent chance that the random variable will take on a value between 40 and 60.
a. To find the probability that the random variable will assume a value between 45 and 55, we need to calculate the z-scores for each value and then use a standard normal distribution table or calculator.
The z-score for 45 is:
\(z = (45 - 50) / 5 = -1\)
The z-score for 55 is:
\(z = (55 - 50) / 5 = 1\)
Using a standard normal distribution table or calculator, we find the probability of the random variable assuming a value between 45 and 55 is:
P(-1 < Z < 1) = 0.6827 (to 4 decimals)
As a result, there is a 0.6827 percent chance that the random variable will take a value between 45 and 55.
b. To find the probability that the random variable will assume a value between 40 and 60, we again need to calculate the z-scores for each value and then use a standard normal distribution table or calculator.
The z-score for 40 is:
\(z = (40 - 50) / 5 = -2\)
The z-score for 60 is:
\(z = (60 - 50) / 5 = 2\)
Using a standard normal distribution table or calculator, we find the probability of the random variable assuming a value between 40 and 60 is:
P(-2 < Z < 2) = 0.9545 (to 4 decimals)
Hence, there is a 0.9545 percent chance that the random variable will take on a value between 40 and 60.
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It is given that y varies directly as x. If y = 5 when x = 4 determine the constant of variation.
Answers
When y changes directly as x, the variation constant is 5/4.
What is constant of variation?In a direct variation, the ratio of two variables; in an inverse variation, the product of two variables. The constant of variation k is used in the direct variation equations = k and y = kx, as well as the inverse variation equations xy = k and y =. A constant of variation (k) is a ratio that shows the connection between the independent and dependent variables (x and y) (y). If both variables have known values, it may be determined by dividing y by x. The constant of variation is the number that connects two variables that are either directly or inversely proportional to each other.
Here,
When one thing varies to another there is always a constant of variation. direct variation it is; y = kx
use the x,y values to find k
5 = 4k
5/4 = k
The constant of variation when y varies directly as x is 5/4.
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prove: an odd number squared is an odd number
Answers
Answer:
2(2n² + 2n) + 1
Step-by-step explanation:
(2n + 1)² can also written as
(2n + 1) × (2n + 1)
= 4n² + 2n + 2n + 1
= 4n² + 4n + 1
= 2(2n² + 2n) + 1
= an odd
Hence Proved!
-TheUnknownScientist 72
At a coffee shop, the first 100 customers’ orders were as follows…
Find the probability a customer ordered a hot drink, given that they ordered a large.
Answers
Today only, a table is being sold at a 36% discount. The sale price is $592. What was the price yesterday?
Answers
The price of the table yesterday is $925
Explanation:The sale price of the table today = $592
Let yesterday's sale price be x
Discount = 36%
The percentage sale price today = 100% - 36%
The percentage sale price today = 64%
Today's sale price = 64% of yesterday's sale price
592 = (64/100)x
592 = 0.64x
x = 592/0.64
x = $925
The price of the table yesterday is $925
11) Forty percent of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random: 1. What is the probability all three of the selected homes have a security system? 2. What is the probability none of the three selected homes have a security system? 3. Did you assume the events to be dependent or independent?
Answers
Answer:
1) Pr(all three) = 0.064
2) Pr(none) = 0.216
3) Independent event
Step-by-step explanation:
Let Probability of homes constructed in the Quail Creek area with a security system = Pr (security)
Where Pr = probability
This is a binomial distribution problem. There ate only two outcomes in this distribution: a success and a failure
Where p = success, q = failure
For n trials,
Pr(X = x) = n!/[(n-x)!x!] × p^x × q^(n-x)
Pr (security) = 40% = 0.4
p = 0.4
q = 1-p = 1-0.4 = 0.6
Numbers selected at random = n = 3
See attachment for more details on the workings.
1) Probability all three of the selected homes have a security system = Pr(all three)
Pr(all three) = 1× (0.4)³ (0.6)^0 = 0.4³
= 0.4×0.4×0.4
Pr(all three) = 0.064
2) Probability none of the three selected homes have a security system
= Pr(none)
Pr(none) = 1 × (0.4)^0 × (0.6)³
= 0.6³ = 0.6×0.6×0.6
Pr(none) = 0.216
3) The events were assumed to be independent as the selection of one house doesn't affect the outcome of the selection of another.
On one day in January, the temperature in Milwaukee, Wisconsin fell 12°F from the high temperature to a low temperature of -8°F. If t represents the high temperature, what is the value of t?
Answers
Answer:
t = 4
Step-by-step explanation:
you have -8 and twelve you equation is x -12 = -8 so we just have to flip the equation around to make it x = 12 -8 which is easy . You just have to make sure you don't get mixed up while flipping the signs.
The value of t is 4.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
The temperature in January = 12 °F
And the low temperature is = -8 °F
The equation of temperature t can be given as
t= high temperature + low temperature
t= 12 - 8
t=4
The value of t is 4.
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Is {[( P ∧ q → R → P → q → R )]} tautology?
Answers
Yes, this series is {[( P ∧ q → R → P → q → R )]} tautology because a tautology is a formula or statement that is true in all possible interpretations. For example, "x = y or x ≠ y".
A tautology is a formula or statement that is true in all possible interpretations. For example, "x = y or x ≠ y". Similarly, "Either the ball is green or the ball is not green" is always true regardless of the color of the ball.
Such a formula can be true or false based on the value assigned to its set variable. The turnstile double notation S is used to indicate that S is a tautology. Tautology is sometimes symbolized by "Vpq", and contradiction by "Opq". The tee (Τ) symbol is sometimes used to denote an arbitrary tautology, with the dual symbol representing an arbitrary contradiction; in any symbolism, a tautology may be substituted for the truth value "true", as symbolized, for instance, by "1".
Tautologies are a key concept in propositional logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. A key property of tautologies in propositional logic is that an effective method exists for testing whether a given formula is always satisfied (equiv., whether its negation is unratifiable).
The definition of tautology can be extended to sentences in predicate logic, which may contain quantifiers—a feature absent from sentences of propositional logic. Indeed, in propositional logic, there is no distinction between a tautology and a logically valid formula. In the context of predicate logic, many authors define a tautology to be a sentence that can be obtained by taking a tautology of propositional logic, and uniformly replacing each propositional variable by a first-order formula (one formula per propositional variable). The set of such formulas is a proper subset of the set of logically valid sentences of predicate logic.
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how much do prices vary for filling a cavity? to find out, an insurance company randomly selects 10 dental practices in california and asks for the cash (non-insurance) price for this procedure at each practice. the interquartile range is $74. identify the statistic.
Answers
The statistic is interquartile range.
Interquartile range is a measure of dispersion that is calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3). To calculate the interquartile range for the 10 dental practices, the insurance company first needs to organize the cash (non-insurance) prices for the procedure at each practice in ascending order. The lower quartile (Q1) is the median of the first 5 values and the upper quartile (Q3) is the median of the last 5 values. The interquartile range is then calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3). In this case, the interquartile range is $74
The interquartile range is the range of values between the 25th and 75th percentiles. In this case, the statistic is the interquartile range for the cash price for filling a cavity across 10 dental practices in California. The interquartile range is $74, meaning that the price for filling a cavity at the 25th percentile is $74 lower than the price at the 75th percentile.
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Which expression is in it’s simplest form
Answers
Answer:
B
Step-by-step explanation:
What are the coordinates of D’ when the quadrilateral is reflected across the line y = x?
On a coordinate plane, quadrilateral A B C D has points (1, 2), (2, 4), (4, 3), (3, 1).
(1, 3)
(2, 4)
(3, 4)
(1, 1)
Answers
Answer:
(1, 3)
Step-by-step explanation:
If quadrilateral ABCD is reflected across the line y = x, then the x- and y-coordinates get reversed. Since the coordinates of point D are (3, 1), then the coordinates of point D' are (1, 3).
Answer:
its a its aaaa itsssssssssssssssssssssss aaaaaaaa sorry im just in a good mood
Step-by-step explanation:
which two types of potential energies would be types of mechanical energies?
1. electrical and kinetic
2.nuclear and chemical
3.radiant and thermal
4.elastic and gravitational
Answers
Answer:
D) elastic and gravitational
Step-by-step explanation:4.elastic and gravitational
Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position).
Answer:
D
Step-by-step explanation:
r - 7 = 1
can someone help me with this
Answers
Answer:
\(r=8\)
Step-by-step explanation:
\(r-7=1\) add seven to both sides
\(r=1+7\\r=8\)
Hope this helps
Answer:
The correct answer to this problem is r = 8.
Step-by-step explanation:
To solve this problem, we have to remember that our goal is to get the variable (in this case, r) by itself on one side of the equation. To do this, we have to get rid of the -7 on the left side of the equation. Therefore, our first step is to add 7 to both sides of the equation. This gives us:
r - 7 = 1
r - 7 + 7 = 1 + 7
r = 8
Thus, your answer is r = 8.
Hope this helps!
Please Anwser This
f(x)=-5x-10 (0,10)
Answers
Answer:
(9, 7)
(1, 3)
(6, -3)
A car dealer reported a 7.5% drop in sales from 895 cars. How many cars were sold?
Answers
Answer:
its is 38.6
Step-by-step explanation:
A farmer owns a total of 10 acres of land. The land is separated into 4 2/3 equally sized sections. How many acres are in each section? Write your answer as a mixed number in simplest form.
Answers
Answer:
2 1/7 arces are in each section
Step-by-step explanation:
4 2/3 is same as 14/3
So we want to divide 10 acres into 14/3 equally sized sections
Mathematically, that will be;
10/14/3
= 10/14 * 3 = 15/7 = 2 1/7 arces
WILL GIVE BRAINLIST TO BEST ANSWER
find the value of x
6 and 8
Answers
The value of x from the given figures are :
6) -6 and 8) -6.
Given two figures of the triangle with two of the sides are extended to form the exterior angle also.
6) One of the angle is equal to 54°.
Since two sides are equal, opposite angles to those sides are also equal.
So the unknown angle opposite on of the equal side is also 54°.
Using the triangle sum property,
m ∠2 = 180° - (54° + 54°) = 72°
Given equation is,
m ∠2 = x + 78
72 = x + 78
x = 72 - 78 = -6
8) Using the same method, oppsoite angles to opposite sides will be equal.
Using the triangle sum property, Interior angle corresponding to ∠2 is,
Interior angle = 180° - (72° + 72°) = 36°
We have to find the exterior angle.
We know that,
Sum of an exterior and interior angle at a vertex = 180°
So,
m ∠2 = 180° - 36° = 144°
Given equation is,
m ∠2 = x + 150
144 = x + 150
x = -6
Hence for both the values of x is -6.
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Marian Plunket owns her own business and is considering an investment. if she undertakes the investment, it will pay $28,000 at the end of each of the new 3 years. the opportunity requires an initial investment of $7,000 plus an additional investment at the end of the second year of $35,000. what is the NPV of this opportunity if the interest rate is 8% per year? Should Marian take it?
Answers
The NPV is positive, it is worth taking the Investment.
Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.
This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:
NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.
The given problem can be solved by using the following steps:
Calculate the present value (PV) of the expected cash inflows:
Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82
Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39
Since the NPV is positive, it is worth taking the investment.
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